As said above, it's to do with the frequencies of the strings being cancelled out by the sympathetic frequencies of the body. You can move them about using weights on the headstock/in the body cavities but you can never completely remove them. Most guitars suffer from it to a greater or lesser extent.
I've found that playing a guitar more, so it really opens up, can reduce the effect somewhat. Basically, play the snot out of it if it's a great guitar and it'll get better. If it's really bad to begin with though, you'd be better off selling it and buying something else.